I've heard that the DOT does indeed respond .... but it seems like a credit card dispute would be more effective.
I'm sure DOT will respond, even if only acknowledging receipt of the complaint, but will they get LH to pay out the refund? As to CC charge-back, I'm not yet prepared to do that because I'm looking at two more canceled LH flights for June and I don't relish the prospect of being in constant fights with LH.